The triggered ability triggers both when Bloodhall Priest enters the battlefield and whenever it attacks. You don’t have to choose only one.

7/13/2016

If you have a card in hand at the moment the trigger condition occurs, Bloodhall Priest’s ability won’t trigger, even if you can get that card out of your hand right afterward. If you have a card in hand as the ability resolves, it has no effect. No damage will be dealt.